Wondering where you are located. It’s just after 4 AM in the UK, so probably not there, but it’s only 8 PM where I am in California. I’ve done cryptics a long time, but took me awhile to get used to British stuff. Yes, there is a city in England called Ely and it has a famous cathedral. Here, however, the desperately seems to me to indicate an anagram. So try different arrangements of e, l, y in the last three spots, or possibly c, e, l, y with the c being for college. If you hit on ???ycle, then you might see bicycle as a possible word, and you go ah, Bic pen! Took me some messing around just like this to figure it out. Tricky clue. There are probably easier ones in this puzzle.